Here is a list of websites that I usually go to in order to download .pdf files of music sheets for anime songs (themes and soundtracks). Some of these websites also offer sheet music for video games. Sites are written in no specific order.

note: I only play the piano and violin. That is why, some of these sites are specifically for violin and/or piano. If you play other instruments such as guitar, cello, flute, etc., these websites also offer links to other wonderful sites to get music sheets for other instruments and guitar tabs.